How Does Floating-Point Precision Affect Integer Results When Using the C `pow` Function?

Floating-Point Precision and Truncation in C

In C , the pow function takes two double-precision floating-point values as input and returns a double-precision floating-point result. However, when dealing with large exponent values, the floating-point precision can lead to unexpected results.

The Problem with pow(10,5)

Consider the following code:

const int sections = 10;

for (int t = 0; t < 5; t++) {
  int i = pow(sections, 5 - t - 1);  
  cout << i << endl;
}

The expected output for this code is:

10000
1000
100
10
1

However, when you run the code, you may encounter an incorrect output:

9999
1000
99
10
1

Understanding the Issue

This discrepancy arises due to the floating-point precision limitations. In C , double-precision floating-point values have a limited number of significant digits (approximately 15-17 decimal digits). When pow(10,5) is computed, the result is a large floating-point value (100000.0). However, when you assign this value to an integer variable (such as i), the fractional part is truncated. Therefore, the value of i becomes 9999 instead of 10000.

Avoiding Precision Issues

To avoid such precision issues, you can use the pow(10.0, 5) directly in the cout statement, which is evaluated as a double-precision floating-point value and rounded when printed:

for (int t = 0; t < 5; t++) {
  cout << pow(sections, 5-t-1) << endl; 
}

This code will produce the correct output:

10000.000000
1000.000000
100.000000
10.000000
1.000000

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